contactanalyses

Contact analyses refer to computational investigations of contact problems in which two or more bodies interact at interfaces under load. They aim to predict contact pressures and areas, deformation, slip or stick behavior, frictional heating, and wear. The analysis must account for non-penetration constraints, possible separation, and the nonlinearities introduced by friction, material behavior, and changing contact configuration. Analyses can be static or dynamic and may involve large deformations, viscoelastic or plastic materials, and complex contact topologies.

Methodologies typically rely on the finite element method and employ various constraint-enforcement strategies. These include penalty methods, Lagrange multipliers, augmented Lagrangian formulations, mortar methods, and Nitsche-type approaches. Friction is usually modeled with Coulomb friction, distinguishing static and kinetic regimes; adhesive contact and rough-surface interactions can also be considered. Key computational challenges involve accurate contact detection, non-smooth transitions between sticking and sliding, mesh sensitivity, and the choice of time integration schemes for dynamic problems. Efficient solvers and parallelization are often important due to the increased system size and nonlinearity.

Applications and validation span many fields. They include gear and bearing contact in mechanical assemblies, brake systems, forming and stamping processes, tire-road interactions, biomechanics (such as joint implants), MEMS devices, and civil engineering connections. Validation typically compares results with Hertzian theory for simple elastic contacts or with experimental measurements. Ongoing developments focus on improving friction models, multi-scale contact, wear prediction, and coupling with thermal and chemical effects.